A uranium nucleus at rest decays into a thorium nucleus and a helium nucleus, as shown below. Which of the following is true?

${{}^{235}}_{92}\mathrm{U}{\to }_{90}^{231}\mathrm{Th}{+}_2^4\mathrm{He}$

1.  Each decay product has the same kinetic energy.

2.  The decay products tend to go in the same direction.

3.  The thorium nucleus has more momentum than the helium nucleus.

4.  The helium nucleus has more kinetic energy than the thorium nucleus.

The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is:

1.  15

2.  30

3.  45

4.  60

For radioactive material, the half-life is 10 minutes. If initially, there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is :

1. 20

2. 10

3. 30

4. 15

When an α– particle of mass m moving with velocity v bombards a heavy nucleus of charge Ze, its distance of closest approach from the nucleus depends on m as:

1. $\frac{1}{\sqrt{\mathrm{m}}}$

2. $\frac{1}{{\mathrm{m}}^2}$

3. m

4. $\frac{1}{\mathrm{m}}$

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then,

1. The nucleus helium has more kinetic energy than the thorium nucleus

2. The helium nucleus has less momentum than the thorium nucleus

3. The helium nucleus has more momentum than the thorium nucleus

4. The helium nucleus has less kinetic energy than the thorium nucleus

A radioisotope 'X' with a half-life 1.4 × 10⁹ years decays to 'Y' which is stable. A sample of the rock from a cave was found to contain 'X' and 'Y' in the ratio 1:7. The age of the rock is :

1. 1.96 x 10⁹ years

2. 3.92 x 10⁹ years

3. 4.20 x 10⁹ years

4. 8.40 x 10⁹ years

A certain mass of Hydrogen is changed to Helium by the process of fusion. The mass defect in the fusion reaction is 0.02866 u. The energy liberated per nucleon is: (Given 1 u = 931 MeV)

If the nuclear radius of ²⁷Al is 3.6 Fermi, the approximate nuclear radius of ⁶⁴Cu in Fermi is:

1. 2.4

2. 1.2

3. 4.8

4. 3.6